I have not built an entire wet dry from scratch from Wal-Mart but while trying to fix mine I managed to find some parts and noticed that I probably could have made an entire wet dry for much less than I paid retail. What you need depends on your application of course. I will describe the most elaborate set-up with bio media chamber. If you use the Berlin method then all you need is a large box that will hold water. Remove the bio tower in my design if this is your filter of choice.
First find a main sump area that will hold the majority of the water. This can be a plastic sweater box or storage bin or in my case a storage box for the back of a pickup truck. They range in price from $3 to $25 dollars. and come in a variety of sizes. You now need a bio chamber of some sort. Why not take a small waste can and cut the bottom out of it. Then cut a "doorway" or series of holes around the bottom so water can flow out into the sump. Probably about an inch above the rim. You can use the bottom of the can if you choose as a drip plate by just punching a bunch of holes into it and then putting into the can. Sometimes the geometry is right and sometimes it isn't and the drip plate will just fall through. If it does (and did in my case) walk over to the garden center. They have these wonderful water drip plates that go under plants to catch the overflow (about $.70) that should do the trick. You can also use one as a support for the bio media but I have found that the plastic grille used for overhead lightings in businesses works best due to its strength. To make life easier I use an Eheim pump for a return to the tank because it can sit directly in the sump water and does not need to sit outside it like some other pumps. A large power head or two would also probably work but I'm not sure about their head pressure. Another idea for a bio chamber: try a plastic bucket (5 gal?).
There are of course other variations such as nesting buckets together in order to provide a drip plate + bio media support etc. Use your imagination but plan before buying anything or else you'll have bought lost of stuff you do not need. If you have any more questions please contact me again. Hope this helps!!